JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let

A_1

and

A_2

be two arithmetic means and

G_1, G_2, G_3

be three geometric means of two distinct positive numbers. Then

G_1^4+G_2^4+G_3^4+G_1^2G_3^2

is equal to

(1) $2(A_1+A_2)G_1G_3$
(2) $(A_1+A_2)G_1^2G_3^2$
(3) $(A_1+A_2)^2G_1G_3$ Official answer
(4) $2(A_1+A_2)G_1^2G_3^2$

Official answer

Option 3

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Arithmetic and Geometric Means

Same idea in other shifts

Asked 4× in all

28 Jun 2022, Shift 2 · Q5If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is $1:7$ and $a+n=33$ , then…MediumSingle correct
3 Aug 2021, Shift 2 · Q67If ' $m$ ' is the arithmetic mean of two distinct real numbers $l$ and $n$ $(l, n > 1)$ and $G_1$ , $G_2$ and $G_3$ are three geometric means…MediumSingle correct
3 Sep 2020, Shift 2 · Q73If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $4^{th}$ A.M. is equal to $2^{nd}$ …MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.